Object with faces that intersect adjacent faces
For that particular example, you could merge near vertices:


Select all (A)
Remove doubles (W> Remove doubles)
Increase merge distance (F6> Merge distance) until the adjacent vertices are all merged.


Once you do that, you will still have internal faces. To get rid of them:


Press Interior faces in 3D view > Header > Select to select internal faces.
Delete them (Delete> Faces)